HYSICL
`HAMACY
`
`LP MARTIN
`
` MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 1
`
`

`
`FOURTH EDITION
`
`Physical Pharmacy
`
`PHYSICAL CHEMICAL PRINCIPLES IN THE PHARMACEUTICAL SCIENCES
`
`Alfred Martin, Ph.D.
`Emeritus Coulter R. Sublett Professor
`Drug Dynamics Institute,
`College of Pharmacy,
`University of Texas
`
`with the participation of
`PILAR BUSTAMANTE, Ph.D.
`Titular Professor
`Department, of Pharmacy
`and Pharmaceutical Technology,
`University Alcala de Henares,
`Madrid, Spain
`
`and with illustrations by
`A. H. C. CHUN, Ph.D.
`Associate Research Fellow
`Pharmaceutical Products Division,
`Abbott Laboratories
`
`Q
`
`B. I. Waverly Pvt Ltd
`New Deihi
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 2
`
`

`
`B. I. Waverly Pvt Ltd
`54 Jsnputh. New Delhi - 110 001
`
`Reprint authorised by Waverly International
`
`Copyright 0 1993 Waverly International. 428 East Preston Street,
`Baltimore, Maryland 2102-3993 USA
`
`Indian Reprint 1994
`Reprint 1995
`
`All rights reserved. This book is protected by copyrighL No part of this book may
`be reproduced in any form or by any means, including photocopying or utilized by
`any infonnation storage and retrieval system without written permission from the
`copyright owner. Violators will be prosecuted.
`
`This edition is for sale in India, Bangladesh, Nepal. Bhutan and Maldives only:
`
`ISBN 81-7431-001-0
`
`Price Rs1495.m
`
`Published in India by 13.1. Waverly Pvt Ltd, 54 Janpath. New Delhi - I10 001 and
`printed at United lnfia Press. New Delhi.
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 3
`
`

`
`2
`
`States of Matter
`
`Binding Forces Between Molecules
`States of Matter
`The Gaseous State
`
`Solids and the Crystalline State
`The Liquid Crystalline State
`Phase Equilibria and the Phase Rule
`Thermal Analysis
`The Liquid State
`
`
`BINDING FORCES BETWEEN MOLECULES
`
`In order for molecules to exist in aggregates in gases,
`liquids, and solids, intermolecular forces must exist. An
`understanding of intermolecular forces is important in
`the study ofpharmaceutical systems and follows logi-
`cally from the previous discussion of intramolecular
`bonding energies. Cohesion, or the attraction of like
`molecules, and adhesion, or/the attraction of unlike
`molecules, are manifestations of intermolecular forces.
`A knowledge of these forces is important
`for an
`understanding not only of the properties of gases,
`liquids, and solids, but also of interfacial phenomena,
`flocculation in suspensions, stabilization of emulsions,
`compaction of powders in capsules, and the compression
`of granules to form tablets.
`Repulsive and Attractive Forces. When molecules
`interact, both repulsive and attractive forces operate.
`As two molecules are brought close together,
`the
`opposite charges in the two molecules are closer
`together than the like charges and cause the molecules
`to attract one another. When the molecules are brought
`so close that
`the outer charge clouds touch,
`the
`molecules repel each other like rigid elastic bodies.
`_Thus attractive forces are necessary in order that
`molecules cohere; repulsive forces are necessary in
`order that the molecules do not interpenetrate and
`annihilate one another. Moelwyn-Hughes‘ points to the
`analogy between human behavior and molecular phe-
`nomenon. Just as the actions of humans are often
`
`so‘ molecular
`influenced by a conflict of loyalties,
`behavior is governed by attractive and repulsive forces.
`Repulsion is due to the interpenetration of the
`electronic clouds of molecules and increases exponen-
`tially with a decrease in distance between the mole-
`cules. At a certain equilibrium distance, about 3 or 4 X
`10‘3 cm (3 or 4 angstroms), the repulsive and attractive
`22
`
`forces are equal. At-this position, the potential energy
`of the two molecules is a minimum and the system is
`most stable (Fig. 2-1). This principle of minimum
`potential energy applies not only to molecules but to
`atoms and to large objects as well.
`Under the following headings are discussed the
`various types of attractive intermolecular forces.
`Van der Waals Forces. Dipolar molecules frequently
`tend to align themselves with their neighbors, so that
`the negative pole of one molecule points toward the
`positive pole of the next. Thus,
`large groups of
`molecules may be associated through weak attractions
`known as dipole—dipole or Keesom forces. Permanent
`dipoles are capable of inducing an electric dipole in
`nonpolar molecules (which are easily polarizable) in
`order to produce dipole—induced dipole, or Debye,
`interactions, and nonpolar molecules can induce polar-
`
`—Energy:>
`
`Fig. 2-1. Repulsive and attractive energies and net energy as a
`function of the distance between molecules. Note that a minimum
`occurs in the net energy because of the different character of the
`attraction and repulsion curves.
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 4
`
`

`
`5
`
`Solutions of Nonelectrolytes
`
`Concentration Expressions
`Equivalent Weights
`Solutions of Nonelectrolytes
`
`Ideal and Real Solutions
`
`Colligativé Properties
`Molecular Weight Determination
`
`Materials may be mixed together to form a true
`solution, a colloidal solution, or a coarse dispersion. A
`true solution is defined as amixture of two or more
`
`.
`
`components that form a homogeneous molecular disper-
`sion, in other words, a one-phase system, the composi-
`tion of which can vary over a wide range. The terms in
`this definition warrant further comment, and an at-
`tempt at clarification is made in the following para-
`graphs.
`A system is a bounded space or a definite quantity of
`substance that is under observation and experimenta-
`tion. Under some circumstances,
`the sytem may
`consist only of radiant energy or an electric field,
`containing no material substances. The term phase has
`already been defined in Chapter 2 as a distinct homo-
`geneous part of a system separated by definite bound-
`aries from other parts of the system. Each phase may
`be consolidated into a contiguous mass or region, such
`as a single piece of ice floating in water, or it may be
`distributed as small particles throughout the system,
`such as oil droplets in an emulsion or solid particles in a
`pharmaceutical suspension. .
`.
`These latter two are examples of coarse dispersions
`the diameter of the particles in emulsions and suspen-
`sions for the most part being larger than 0.1 pm (100 A
`or 10" cm). A colloidal dispersion represents a system’
`having a particle size intermediate between that of a
`true solution and a coarse dispersion, roughly 10 to 5000
`A. A colloidal dispersion may be considered as a
`two-phase system (heterogeneous) under certain cir-
`cumstances and as a one-phase system (homogeneous)
`under others. A colloidal dispersion of silver proteinate
`in water is heterogeneous since it consists of distinct
`particles constituting a separate phase. A colloidal
`dispersion of acacia or sodium carboxymethylcellulose
`in water, on the other hand, is homogeneous. It does
`not differ significantly from a solution of sucrose and
`
`may be considered as a single-phase system or true
`solution.‘
`_
`A solution composed of only two substances is known
`as a binary solution, and the components or constitu-
`ents are referred to as the solvent and the solute. We
`
`use the terms component and constituent interchange-
`ably here, as do other authors, to represent the pure
`chemical substances that make up a solution. The
`number of components has a definite significance in the
`"phase rule, as explained on p. 37. The constituent
`present in the greater amount in a binary solution is
`arbitrarily designated as the solvent and the constitu-
`ent in the lesser amount as the solute. When a solid is
`
`dissolved in a liquid, however, the liquid is usually
`taken as the solvent and the solid as the solute,
`irrespective of the relative amounts of the constituents.
`When water is one of the constituents of a liquid
`mixture, it is usually considered the solvent. When
`dealing with mixtures of liquids that are miscible in all
`proportions, such as alcohol and water,
`it
`is less
`meaningful to classify the constituents as solute and
`solvent.
`
`Properties of Solutions. The physical properties of
`substances may be classified as colligative, additive,
`and constitutive. Some of the constitutive and additive
`
`properties of molecules were considered in Chapter 4.
`In the field of thermodynamics, physical properties of
`systems are classified as extensive properties, depend-
`ing on the quantity of the matter in the system (e.g.,
`mass and volume) and intensive properties, which are
`independent of the amount of the substances in the
`system (e.g., temperature, ‘pressure, density, surface
`tension, and viscosity of a pure liquid).
`Colligative properties depend mainly on the number
`of particles in a solution. The colligative properties of
`solutions are osmotic pressure, vapor pressure lower-
`ing, freezing point depression, and boiling point eleva-
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 5
`
`

`
`102 Physical Pharmacy
`
`tion. The values of the colligative properties are
`approximately the same for equal concentrations of
`different nonelectrolytes in solution regardless of the
`species or chemical nature of’ the constituents.
`In
`considering the colligative properties of solid-in-liquid
`solutions, it is assumed that the solute is nonvolatile
`and that the pressure of the vapor above the solution is
`provided entirely by the solvent.
`Additive properties depend on the total contribution
`of the atoms in the molecules or on the sum of the
`
`properties of the constituents in a solution. An example
`of an additive property of a compound is the molecular
`weight, that is, the sum of the masses of the constituent
`atoms.
`
`The masses of the components of a solution are also
`additive, the total mass of the solution being the sum of
`the masses of the individual components.
`Constitutive properties depend on the arrangement
`and to a lesser extent on the number and kind of atoms
`
`within a molecule. These properties give clues to the
`constitution of individual compounds and groups of
`molecules in a system. Many physical properties may be
`pa.rtly additive and partly constitutive. The refraction
`of light, electric properties, surface and interfacial
`characteristics, and the solubilityof drugs areat least
`in part constitutive and in part additive properties;
`these are considered in other sections of the book.
`Types of Solutions. A solution may be classified
`according to the states in which the solute and solvent
`occur, and since three states of matter (gas, liquid, and
`crystalline solid) exist, nine types of homogeneous
`mixtures of solute and solvent are possible. These
`types, together with some examples, aregiven in Table
`5- 1.
`.
`
`When solids or liquids dissolve in a gas to form a
`gaseous solution, the molecules of the solute can be
`treated thermodynamically like a gas; similarly, when
`gases or solids dissolve in liquids, the gases and the
`solids can be considered to exist in the liquid state. In
`the formation of solid solutions, the atoms of the gas or
`liquid take up positions in the crystal lattice and behave
`like atoms or molecules of solids.
`
`The solutes (whether gases, liquids, or solids) are
`divided into two main classes: nonelectrolytes and
`electrolytes. Nonelectrolytes are substances that do not
`yield ions when dissolved in water and therefore do not
`
`TABLE 5- 1. min of solutions
`
`Solute
`
`Gas
`Liquid
`Solid
`Gas
`Liquid
`Solid
`Gas
`Liquid
`Solid
`
`Solvent
`
`Example
`
`Gas
`Gas
`Gas
`Liquid
`Liquid
`Liquid
`Solid
`Solid
`Solid
`
`Air
`Water in oxygen
`Iodine vapor in air
`Carbonated water
`Alcohol in water
`Aqueous sodium chloride solution
`Hydrogen in palladium
`Mineral oil in paraffin
`Go|d—si|ver mixture, mixture of alums
`
`conduct an electric current through the solution. Ex-
`amples of nonelectrolytes are sucrose, glycerin, naph-
`thalene, and urea. The colligative properties of solu-
`tions of nonelectrolytes are fairly regular. A 0.1-molar
`solution of a nonelectrolyte produces approximately the
`same colligative effect as any other nonelectrolytic
`solution of equal concentration. Electrolytes are sub-
`stances that form ions in solution, conduct the electric
`current, and show apparent “anomalous” colligative
`properties, that is, they produce a considerably greater
`freezing point depression and boiling point elevation
`than do nonelectrolytes of the same concentration.
`Examples of electrolytes are hydrochloric acid, sodium
`sulfate, ephedrine, and phenobarbital.
`Electrolytes may be subdivided further into strong
`electrolytes and weak electrolytes depending on
`whether the substance is completely or only partly
`ionized in water. Hydrochloric acid and sodium sulfate
`are strong electrolytes, whereas ephedrine and phe-
`nobarbital are weak electrolytes. The classification of
`electrolytes according to Arrhenius and the discussion
`of the modern theories of electrolytes are found in
`Chapter 6.
`
`CONCENTRATION EXPRESSIONS
`
`The concentration of a solution may be expressed
`either in terms of the quantity of solute in a definite
`volume of solution or as the quantity of solute in a
`definite mass of solvent or solution. The various
`expressions are summarized in Table 5-2.
`Molarity and Normality.’ Molarity and normality are
`the expressions commonly used in analytical. work. All
`solutions of the same molarity contain the same number
`of solute molecules in a definite volume of. solution.
`When a solution contains more than one solute, it may
`have different molar concentrations with respect to the
`various solutes. For example, a solution can be 0.001
`molar (0.001 M) with respect to phenobarbital and 0.1
`M with respect to sodium chloride. One liter of such a
`solution is prepared by adding 0.001 mole of phenobar-
`bital (0.001 mole X 232.32 g/mole = 0.2323 g) and 0.1
`mole of sodium chloride (0.1 mole X 58.45 g/mole =
`5.845 g) to enough water to make 1000 mL of solution.
`Difficulties are sometimes encountered when one
`
`desires to express the molarity of an ion or radical in a
`solution.-A molar solution of sodium chloride is 1 M with
`respect to both the sodium and the chloride ion,
`whereas a molar solution of Na2CO3 is 1 M with respect
`to the carbonate ion and 2 M with respect to the sodium
`ion, since each mole of this salt contains 2 moles of
`sodium ions. A molar solution of sodium chloride is.also
`1 normal (1 N) with respect to bothits ions; however, a
`molar solution of sodium carbonate is 2 N with respect
`to both the sodium and the carbonate ion.
`
`Molar and normal solutions are popular in chemistry
`since they may be brought to a convenient volume; a
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 6
`
`

`
`TABLE 5-2.
`
`concentmtion Expressions
`
`Expression
`
`Symbol Definition
`
`Chapter 5 - Solutions ofNmwlectrolytes
`
`103
`
`Molarity
`Normality
`Molality
`Mole fraction
`
`Mole percent
`
`Moles (gram molecular weights) of solute in 1 liter of solution
`Gram equivalent weights of solute in 1 liter of solution
`Mo|es of solute in 1000 g of solvent
`Ratio of the moles of one constituent (e.g.. the solute) of a solution
`to the total moles of all constituents (solute and solvent)
`Moles of one constituent in 100 moles of the solution. Mole percent
`is obtained by multiplying mole fraction by 100.
`% w/w Grams of solute in 100 g of solution
`Percent by weight
`% v/v Milliliters of solute in 100 mL of solution
`Percent by volume
`Percent weight-in-volume %*w/v Grams of solute in 100 mL of solution
`Milligram percent
`—
`Milligrams of solute in 100 mL of solution
`
`M, c
`N
`m
`X, N
`
`. 4.
`
`,
`
`volume aliquot of the solution, representing a known
`weight of solute, is easily obtained. by the use of the
`burette or pipette.
`Both molarity and normality have the disadvantage
`of changing value with temperature because of the
`expansion or contraction of liquids, and should not be
`used when one wishes to study the properties of
`solutions at various temperatures. Another difficulty
`arises in the use of- molar and normal solutions for the
`
`study of properties such as vapor pressure and osmotic
`pressure, which are related to the concentration of the
`solvent. The volume of the solvent in a molar or a
`
`normal solution is not usually known, and it varies for
`different solutions of the same concentration, depend-
`ing upon the soluteand solvent involved.
`Molality. A molal solution is prepared in terms of
`weight units and does not have the disadvantages just
`discussed; therefore, molal concentration appears more
`frequently than molarity and normality in theoretic
`studies. It is possible to convert molality into molarity
`or normality if the final volume of the solution is
`observed or if the density is determined. In aqueous
`solutions more dilute than 0.1 M, it usually may be
`assumed for practical purposes that molality and mo-
`larity are equivalent. For example, a 1% solution by
`weight of sodium chloride with a specific gravity of
`- 1.0053 is 0.170 M and 0.173 molal (0.173 m). The
`following difference between molar and molal solutions
`should also be noted. If another solute, containing
`neither sodium nor chloride ions, is added to a certain
`volume of a molal solution of sodium chloride,
`the
`solution remains 1 m in sodium chloride, although the
`total volume and the weight of the solution increase.
`Molarity, of course, decreases when another solute is
`added because of the increase in volume of the solution.
`
`Molal solutions are prepared by adding the proper
`weight of solvent to the carefully weighed quantity of
`the solute. The volume of the solvent can be calculated
`
`from the specific gravity, and the solvent may then be
`measured from a burette rather than weighed.
`Mole Fraction. Mole ,f1-action is used frequently in
`experimentation involving theoretical considerations
`since it gives a measure of the relative proportion
`
`of moles of each constituent
`
`in a solution.
`
`It
`
`is
`
`expressed as
`
`7&1
`X1- M + M
`77/2
`X2 - nl + "2
`
`(5-1)
`
`(5-2)
`
`for a system of two contituents.
`X1 is the mole fraction of constituent 1 (the subscript
`1 is ordinarily used as the designation for the solvent),
`X2 is the mole fraction of constituent 2 (usuallythe
`solute), and n, and re, are the number ofmoles of the
`constituents in the solution. The sum of the mole
`
`fractions of solute and solvent must equal unity. Mole
`fraction is also expressed in percentage terms’ by
`multiplying X1 or X2 by 100. In a solution containing
`0.01 mole of solute and 0.04 mole of solvent, the mole
`fraction of the solute X2 = 0.01/(0.04 + 0.01) = 0.20.
`Since the mole fractions of the two constituents must
`
`equal 1, the mole fraction of the solvent is 0.8. The mole
`percent of the solute is 20%; the mole percent of the
`solvent is 80%.
`The manner in which mole fraction is defined allows
`one to express the relationship between the number of
`solute and solvent molecules in a simple, direct way. In
`the example just given, it is readily seen that two out of
`every 10 molecules in the solution are solute molecules,
`and _it will be observed later that many of the properties
`of solutes and solvents are directly related to theirimole
`fraction inthe solution. For example, the partial vapor
`pressure above asolution brought°about by the pres-
`ence of a volatile solute is equal to the vapor pressure of
`the pure solute multiplied by the mole fraction of the
`solute in the solution.
`
`The percentage method of
`Percent Expressions.
`expressing the concentration of pharmaceutical’ solu-
`tions is quite common. Percent _by weight signifies the
`number of grams of solute per 100 grams of solution. A
`10% by weight (% w/w) aqueous solution of glycerin
`contains 10 got’ glycerin dissolved in enough water (90
`g) to make 100 g of solution. Percent by volume is
`expressed as the volume of solute in milliliters con-
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 7
`
`

`
`TABLE 5-3.
`
`conversion Equations for concentration Terms
`
`A. Molality (moles of solute/kg of_ solvent, m) and mole fraction of
`solute (X2).
`“
`
`X =
`
`2
`
`m
`
`+ EM?‘-Q
`
`1000 X2
`m = M1(1 — X2)
`
`«
`
`_ 1000 (1 — x1)
`_T
`B. Molarity (moles of solute/liter of solution, c) and mole fraction of
`solute (X2).
`
`Xz=
`
`C
`
`1000p — cM2
`c + ———j
`M1
`
`C
`
`1000 pX2
`_
`' M1(1 — x2) + Mgxg
`
`C. Molality (m) and molarity (c).
`
`,,, = _1fl’£_
`1000p - M2 C
`
`C =
`
`10009
`1000
`—— + M;
`m
`
`D’. Molality (m) and molarity (c) in terms of weight of solute, wz,
`weight of solvent, w,, and molecular weight. M2, of solute.
`W2/M2
`1000 wz
`
`= w,/1ooo = w1M2
`1000 pwg
`= rnzm, + w)
`
`m C
`
`Definition of terms:
`p = density of the solution (3/cm’)
`M1 = molecular weight of the solvent
`M2 = molecular weight of the solute
`X1 = mole fraction of the solvent
`X2 = mole fraction of the solute
`w; = weight of the solvent (3. mg, kg, etc.)
`we = weight of the solute (g, mg, kg. etc.)
`
`Example 5-1 are useful to determine whether your
`derived equation is correct.
`
`EQUIVALENT WEIGHTS’
`
`A gram atom of hydrogen weighs 1.008 g and consists
`of 6.02 X 10” atoms (Avogadro's number) of hydrogen.
`This gram atomic weight of hydrogen combines with
`6.02 X 1023 atoms of-fluorine and with half of 6. 02 X 1023
`atoms of oxygen. One gram atom of fluorine weighs 19
`g and one gram atom of oxygen weighs 16 g. Therefore,
`1.008 g of hydrogen combines with 19 grams of fluorine
`and with half of 16 or 8 grams of oxygen. The quantities
`of fluorine and oxygen combining with 1.008 g of
`hydrogen are referred to as the equivalent weight of
`the combining atoms. One equivalent (Eq) of fluorine
`(19 g) combines with 1.008 g of hydrogen. One equiva-
`
`l04 Physical Pharmacy
`
`tained in 100 mL of the solution. Alcohol (USP) contains
`92.3% by weight and 94.9% by volume of CZHEOH at
`15.56°, that is, it contains 92.3 g of C2H5OH in 100 g of
`solution or 94.9 mL of C2H50H in 100 mL of solution.
`calculations Involving concentration Expressions. The
`calculations involving the various concentration expres-
`‘ sions are illustrated in the following example.
`
`ExampIe'5— I. An aqueous solution of exsiccated ferrous sulfate was
`prepared by adding 41.50 g of FeSO_, to enough water to make 1000
`mL of solution at 18° C. The density of the solution is 1.0375, and the
`molecular weight of FeSO., is 151.9. Calculate (a) the molarity; (b) the
`molality; (c) the mole fraction of FeS0., the mole fraction of water,
`and the mole percent of the two constituents; and (cl) the percent by
`weight of FeS0,.
`(a) Molarity
`
`Moles of FeSO4 =
`
`g of FeS04
`molecular weight
`
`41.50 _
`" 151.9 ' 02732
`
`_
`M°"*"‘y '
`(b) Molality
`
`moles of FeS04
`
`0,2732 _
`- 1 liter * “-2732 M
`
`Grams of solution = volume X density;
`1000 X 1.0375 = 1037.5 g
`Grams of solvent = grams of solution — grams
`ofFeS0., = 1037.5 — 41.5 =_ 996.0 g
`
`0,2732
`moles of FeSO4
`_
`M°"1“" ‘ kgof solvent ‘ 0.990 ' 02743 "‘
`(c) Mole fraction and mole percent
`996
`
`=
`
`Moles of water =
`Mole fraction of FeSO,,
`moles of FeSO4
`02732
`X‘ ' moles + moles ' 55.27 + 0.2732 ' M049
`water
`FeS04
`
`moles
`
`Mole fraction of water,
`
`55.27
`X‘ ' 55.27-+ 0.2732 E 0'99“
`Notice that X, + X, = 0.9951 + 0.0049 = 1.0000
`Mole percent of FeS04 = 0.0049 x 100 = 0.49%
`Mole percent of water = 0.9951 X 100 = 99.51%
`(41) Percent by weight
`Percent by weight of FeS0.
`
`_ g of F‘eS04
`_ g of solution X 100
`
`= lgfi x 100 = 4.00%
`
`One may use the table of conversion equations, Table
`5-3, to convert concentration expressions, say molal-
`ity, into its value in molarity or mole fraction. Or,
`knowing the weight w, of a solvent, the weight wz of the
`solute, and the molecular weight M2 of the solute, one
`can calculate the molarity c or the molality m of the
`solution. As an exercise, the reader should derive an
`expression relating X1 to X2 to the weights w, and w2
`and the solute’s molecular weight M2. The data in
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 8
`
`

`
`1O
`
`Solubility and Distribution Phenomena
`
`General Principles
`So|vent—So|ute Interactions
`
`Solubility of Gases in Liquids
`Solubility of Liquids in Liquids
`
`Solubility of Nonionic Solids in Liquids
`Distribution of Solutes Between immiscible
`Solvents
`
`The topic of solutions was introduced in Chapter 5.
`We must now look at solutions in a more quantitative
`manner so as to understand the theory and applications
`of the phenomenon of solubility. Such knowledge is
`important to the pharmacist, for it permits him to
`choose the best solvent medium for a drug or combina-
`tion of drugs, helps in overcoming certain difficulties
`that arise in the preparation of pharmaceutical solu-
`tions, and, furthermore, can serve as a standard or test
`of purity. A detailed study of solubility and related
`properties also yields information about the structure
`and intermolecular forces of drugs.
`The solubility of a compound depends upon the
`physical and chemical properties of the solute and the
`solvent, as well as upon such factors as temperature,
`pressure, the pH of the solution, and, to a lesser extent,
`the state of subdivision of the solute.
`
`Of the nine possible types of mixtures, based on the
`three states of matter (p. 102), only gases in liquids,
`liquids in liquids, and solids in liquids are of particular
`pharmaceutical importance and will be considered in
`this chapter.
`
`GENERAL PRINCIPLES
`
`Definitions. A saturated solution is one in which the
`
`solute is in equilibrium with the solid phase (solute).
`Solubility is "defined in quantitative terms as the
`concentration of solute in a saturated solution at a
`
`certain temperature, and in a qualitative way, it may be
`defined as the spontaneous interaction of two or more
`substances to form a homogeneous molecular disper-
`sion.
`
`An unsaturated or subsaturated solution is one
`
`containing the dissolved solute in a concentration below
`
`212
`
`that necessary for complete saturation at a definite
`temperature.
`A supersaturated solution is one that contains more
`of the dissolved solute than it would normally contain at
`a definite temperature, were the undissolved solute
`present. Some salts such as sodium thiosulfate and
`sodium acetate can be dissolved in large amounts at an
`elevated temperature and, upon cooling, fail to crystal-
`lize from the solution. Such supersaturated solutions
`can be converted to stable saturated solutions by
`seeding the solution with a crystal of solute,‘ by
`vigorous agitation, or by scratching the walls of the
`container. Supersaturation presumably occurs when
`the small nuclei of the solute required for the initiation
`of crystal formation are more soluble than larger
`crystals, making it difficult for the nuclei to form and
`grow with resultant failure of crystallization.
`The Phase Rule. Solubility may be described in a
`concise manner by use of Gibbs’ phase rule, which was
`described on page 37.
`
`F=C—P+2
`
`(10-1)
`
`in which F is the number of degrees offreedom, that is,
`the number of independent variables (usually tempera-
`ture, pressure, and concentration) that must be fixed to
`completely determine the system, C is the smallest
`number of components that are adequate to describe
`the chemical composition of each phase, and P is the
`number of phases. The application'of the phase rule to
`the miscibility of liquids is described on pages 40, 41 and
`the application to solutions of solids in liquids is given
`on p. 41.
`Solubility Expressions. The solubility of a drug may be
`expressed in a number of ways. The U. S. Pharmacopeia
`and National Formulary list the solubility of drugs as
`the number of milliliters of solvent in which 1 gram of
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 9
`
`

`
`TABLE 10-1.
`
`Terms of Approximate Solubility
`
`Term
`
`Very soluble
`Freely soluble
`Soluble
`sparingly soluble
`Slightly soluble
`Very slightly soluble
`Practically insoluble, or insoluble
`
`‘
`
`Parts of Solvent Required
`for 1 Part of Solute
`
`Less than 1 part
`1 to 10 parts
`10 to 30 parts
`30 to 100 parts
`100 to 1000 parts
`1000 to 10,000 parts
`More than 10,000 parts
`
`solute will dissolve. For example, the solubility of boric
`acid is given in the U.S. Pharrnacopeia as follows: 1 g of
`boric acid dissolves in 18 mL of water, in 18 mL of
`alcohol, and in 4 mL of glycerin. Solubility is also
`quantitatively expressed in terms of molality, molarity,
`and percentage (p. 103).
`For substances whose solubilities are not definitely
`known,
`the values are described in pharmaceutical
`compendia by the use of certain general terms, as given
`in Table 10-1. Solubilities of drugs are found expressed
`in various units in the Merck Index. For exact solubil-
`ities of many substances, the reader is referred to the
`works of Seidell, Landolt—Bornstein, International
`Critical Tables, Lange’s Handbook of Chemistry, and
`the CRC Handbook of Chemistry and Physics. Tech-
`niques suitable for accurately determining the solubili-
`ties of solid compounds in liquids and the mutual
`solubilities of two liquids have been described by Mader
`and Grady.‘
`
`SOLVENT—SOLUTE INTERACTIONS
`
`The reader should review pages 22 to 24 in Chap-
`ter 2 on intermolecular forces before continuing with
`this section. The pharmacist knows that water. is a
`good solvent for salts, sugars, and similar compounds,
`whereas mineral oil and benzene are often solvents for
`
`substances that are normally only slightly soluble in
`water. These empiric findings are summarized in the
`statement: “like dissolves like.” Such a maxim is
`
`satisfying to most of us, but the occasional inquisitive
`student may be troubled by this vague idea of “like-
`ness.” If he sets out to learn in what manner the solute
`
`and solvent are alike, he will find himself in a fascinat-
`ing area of scientific investigation that is still in an
`unsettled state. The advanced student who is inter-
`
`ested in this subject may Wish to consult the books by
`Hildebrand and Scott,’ Leussingf’ and Dack.‘
`Polar Solvents. The solubility of a drug is due in large
`measure to the pola.rity of the solvent, that is, to its
`dipole moment. Polar solvents dissolve ionic solutes and
`other polar substances. Accordingly, water mixes in all
`proportions with alcohol and dissolves sugars and other
`polyhydroxy compounds.
`
`Chapter 10 - Solubility and Distribution Phenomena 213
`
`Hildebrand has shown, however, that a consideration
`of dipole moments alone is not adequate to explain the
`solubility of polar substances in water. The ability of
`the solute to form hydrogen bonds is a far more
`influential factor than is the polarity as reflected in a
`high dipole moment. Although nitrobenzene has a
`dipole moment of 4.2 X 10"“ esu cm and phenol a value
`of only 1.7 X 10‘13 esu cm, nitrobenzene is soluble only
`to the extent of 0.0155 mole/kg in water, while phenol is
`soluble to the extent of 0.95 mole/kg at 20° C.
`Water dissolves phenols, alcohols, aldehydes, ke-
`tones, airlines, and other oxygen- and nitrogen-contain-
`ing compounds that can form hydrogen bonds with
`water.
`
`If
`R_0. .
`
`‘F
`. .H_0. .
`
`.
`
`.
`
`Alcohol
`
`ll
`R—C:O. .
`
`ll
`. .H—0. .
`
`. .'
`
`Aldehyde
`
`Amine
`
`A difference in acidic and basic character of the
`
`constituents in the Lewis electron donor—acceptor
`sense also contributes to specific interactions in solu-
`tions.
`
`The molecules of water in ice are joined together by
`hydrogen bonds to yield a tetrahedral structure. Al-
`though some of the hydrogen bonds are broken when
`ice melts, water still retains its ice-like structure in
`large measure at ordinary temperatures. This quasi-
`crystalline structure is broken down when water is
`mixed with another substance that is capable of hydro-
`gen bonding. When ethyl alcohol and water are mixed,
`the hydrogen bonds between the water molecules are
`replaced partly by hydrogen bonds between water and
`alcohol molecules.
`
`In addition to the factors already enumerated, the
`solubility of a substance also depends on structural
`features such as the ratio of the polar to nonpolar
`groups of the molecule. As the length of a nonpolar
`chain of an aliphatic alcohol increases, the solubility of
`the compound in water decreases. Straight-chain mono-
`hydroxy alcohols, aldehydes, ketones, and acids with
`more than four or five carbons cannot enter into the
`
`MYLAN PHARMS. INC. EXHIBIT 1042 PAGE 10
`
`

`
`214 Physical Pharmacy
`
`hydrogen-bonded structure of water and hence are only
`slightly soluble. When additional polar- groups are
`present in the molecule, as found in propylene glycol,.
`glycerin, and tartaric acid, water solubility increases
`greatly. Branching of the carbon chain reduces the
`nonpolar effect and leads to increased water solubility.
`Tertiary butyl alcohol is miscible in all proportions with
`water, whereas n-butyl alcohol dissolves to the extent
`of about 8 g/100 mL of water at 20° C.
`In brief, polar solvents such as water act as solvents
`according to the following mechanisms.‘
`(a) Owing to their high dielectric constant, namely
`about 80 for water, polar solvents reduce the force of
`attraction between oppositely charged ions in crystals
`such as sodium chloride (p. 30). Chloroform has a
`dielectric constant of 5 and benzene one of about 2;
`hence,
`ionic compounds are practically insoluble in
`these solvents.
`
`(b) Polar solvents break covalent bonds of potentially
`strong electrolytes by acid—base reactions since these
`solvents are amphiprotic (p. 143). For example, water
`brings about the ionization of HCl as follows:
`
`HCl +